Question: Solve for $x$ and $y$ using elimination. ${-x-6y = -61}$ ${x-5y = -49}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -110$ $\dfrac{-11y}{{-11}} = \dfrac{-110}{{-11}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-x-6y = -61}\thinspace$ to find $x$ ${-x - 6}{(10)}{= -61}$ $-x-60 = -61$ $-x-60{+60} = -61{+60}$ $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {x-5y = -49}\thinspace$ and get the same answer for $x$ : ${x - 5}{(10)}{= -49}$ ${x = 1}$